Bernoulli’s Equation & Applications Of Bernoulli’s Equation

Bernoulli’s Equation is one of the most versatile equation ever.
This is an important principle involving the movement of a fluid through a pressure difference. Suppose a fluid is moving in a horizontal direction and encounters a pressure difference. This pressure difference will result in a net force, which by Newton’s 2nd law will cause an acceleration of the fluid. The fundamental relation,

bernoulli's equation

in this situation can be written as-

bernoulli's equation

which furthermore can be expressed as

bernoulli's equation

In other words,

bernoulli's equation

This principle is generally known as the conservation of energy principle and states that the total energy of an isolated system remains constant — it is said to be conserved over time. This is equivalent to the First Law of Thermodynamics, which is used to develop the general energy equation in thermodynamics. This principle can be used in the analysis of flowing fluids and this principle is expressed mathematically by the following equation:

Bernoulli's equation

where h is enthalpy, k is the thermal conductivity of the fluid, T is temperature, and Φ is the viscous dissipation function.

Bernoulli’s Equation-

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